Question

Discuss but no need to submit. In statistics one of the most important distributions is the normal distribution. Why is it so important? A normal distribution with mean mu and variance sigma^2 has this probability distribution function: P(x) = 1/[sigma root (2 pi) ] e^(-(x-mu)^2/[2 sigma^2]).

Calculate [dP(x)]/[dx].

Please explain and show calculations :)

Answer 1

pows, .- (2-42 (202) اے = (x)) و م2 (*-) ۔ اے ed Ce)) : - X - 2( - ) da oden 22 AP (n) اورسل- ) ۔ ) 2 ۔ و (س- an Zg3020 محرم - 1 -ے - ) 2- = ( = - راس ف ارس ( 3ے 2

A bell-shaped and symmetrical theoretical distribution, with the mean, median, and mode all coinciding at its peak and with frequencies gradually decreasing at both ends of the curve. The normal distribution is a theoretical ideal distribution. Real-life empirical distributions never match this model perfectly. However, many things in life do approximate the normal distribution, and are said to be "normally distributed". One reason the normal distribution is important is that many psychological and educational variables are distributed approximately normally. Measures of reading ability, introversion, job satisfaction, and memory are among the many psychological variables approximately normally distributed. although the distributions are only approximately normal, they are usually quite close. A second reason the normal distribution is so important is that it is easy for mathematical statisticians to work with. This means that many kinds of statistical tests can be derived for normal distributions. Almost all statistical tests discussed in this text assume normal distributions. Fortunately, these tests work very well even if the distribution is only approximately normally distributed. Some tests work well even with very wide deviations from normality.

Answer 2

Solution A bello shaped and Symmotorical the retical distribution, with the mean, median, and made all coinciding at a peak and cooth forequencies gradevally decreasing at both ends of the curre. The normal distribution is a theoretical ideal distribution Real-life empirical distributions never match this model perfectly. However, many things in life do approximate the normal distribution, and are Baid to be " normally distributed". Ore reason the normal distribution is important is that many psychological and Educational variables are distributed aproximately notmailles, measures of reading abil.ty, introverkron, Bob eatisfaction, and memoy ere among the many Asychological variables approximately normally distaibuted although the distributions are only appaonimately nomal, they are usually gutte clase. A second reason the normal distribution & is so important as that as may for mathematical statisticang to work with. icon This means that many kinds of Camsextatistical tests on the desired 487

normal distributions. Almost all statistical testes discussed in this text assume holmal distai betions. Fortunately, thede testo work very well even of the distribution s only approximately holmally distributed. Some tests work well even with vary wide deviations from nortulky Scanned with CamScanner
please like if it helps me...

Thank you....